When my palms face each other during rowing or pressing movements it feels the most natural and I have zero joint pain. The moment I change to palms up or down I start to feel it in my elbow and wrist joints and even shoulders.
Because of the tear I have in tennis elbow tendon, I mainly do palms facing (parallel) these days. Basil's "Supinator Machine" would not be in my life at this point.
I bench w/ a multi-grip bar (football bar, swiss bar, etc), I use the MAG bar Medium grip (parallel grip), Hammer curls for Bi's, etc. The natural feeling of the MAG's are awesome, even the way they sit in your hand.
And w/ the arch in the bar, you can pull your lats back further at the bottom of the movement, and squeeze/hold. Works well for seated cable rows also.